A convolutional framework for detecting event-driven dynamics in energy price series

Shanghai Composite Index prediction has become a hot issue for many investors and academic researchers. Deep learning models are widely applied in multivariate time series forecasting, including recurrent neural networks (RNN), convolutional neural networks (CNN), and transformers. Specifically, the Transformer encoder, with its unique attention mechanism and parallel processing capabilities, has become an important tool in time series prediction, and has an advantage in dealing with long sequence dependencies and multivariate data correlations. Drawing on the strengths of various models, we propose the CNN-Transformer-LSTM Networks (CTLNet). This paper explores the application of CTLNet for Shanghai Composite Index prediction and the comparative experiments show that the proposed model outperforms state-of-the-art baselines.

Forecasting non-stationary time series remains difficult due to long-range dependencies, local volatility bursts, structural shifts, and nonlinear oscillatory behaviors. Although Transformer-based forecasters are effective for modeling long-term temporal dependencies, their feed-forward blocks typically rely on smooth static activations that are insufficiently sensitive to abrupt regime changes. Motivated by quantitative Transformer designs and oscillator-based nonlinear activations, we propose QFCQT, short for Quantum-Fractal-inspired Chaotically Gated Quantformer, for robust forecasting under complex volatile dynamics. Here, "quantum-fractal-inspired" denotes a computational analogy based on soft oscillator superposition and multi-scale nonlinear responses, rather than a formal quantum-mechanical or fractal-theoretic derivation. QFCQT consists of three main components: (1) a Quantformer-style numerical encoder that directly processes multivariate inputs via linear embedding; (2) a learnable Lee-oscillator activation module that maps scalar pre-activations to dynamic oscillatory responses and summarizes them through Max-over-Time pooling; and (3) a smooth-chaotic gated fusion mechanism that adaptively balances conventional smooth activations and chaos-sensitive responses. Furthermore, instead of using a single fixed oscillator, QFCQT employs a soft superposition of eight parameterized Lee oscillator families to adaptively capture different nonlinear response patterns across regimes. Experiments on ETTh1, ETTh2, and A-share Stock Index benchmarks show that QFCQT consistently outperforms strong baselines, including Informer, LogTrans, LSTMa, HAT, and COTN.

Many natural and engineered time series -- equity returns, climate anomalies, turbulent velocities, neural recordings, packet-level network traffic -- are approximately self-similar: their horizon-$T$ distribution is tied to the horizon-$1$ distribution by one scaling exponent $H$. Standard deep generative sequence models (transformers, dilated TCNs, the WaveNet family) ignore this. Their receptive fields are wide, but kernel parameters live independently at every dilation level, yielding a multi-scale architecture, not a scale-equivariant one. We make three contributions. First, we give a precise definition of discrete scale equivariance for 1D causal networks and prove that dyadic dilation commutes (up to boundary effects) with any dilated-convolution stack whose kernel weights are shared across levels. Tying the kernel shrinks the convolutional parameter budget by an $L$-fold factor (where $L$ is depth) and hard-wires self-similarity in as an inductive bias. Second, we wrap this Scale-Equivariant WaveNet (SE-WaveNet) backbone in three components that carry the same prior: a one-level Daubechies-4 wavelet input, a Hurst-FiLM block exposing the local scaling exponent, and a spectral-consistency training term targeting the $|f|^{-(2H+1)}$ power-law spectrum. The head is a conditional normalising flow, chosen to preserve equivariance. Third, on 30 years of S&P 500 daily log-returns, SE-WaveNet samples reproduce the empirical scaling-collapse diagnostic on the Allan-Variance top-25 universe (median $\mathcal{C}^\star = 0.020$), while a vanilla WaveNet at matched capacity does not ($\geq 0.06$). NLL, KS-calibration, and tail energy distance tie or beat the baseline, with $L\times$ fewer convolutional parameters.